Question

a sample of h decays, leaving 1/32 of the original amount. how long would this take?
20
40
3.1
100
25
1
3
12.3
12.5
61.5
50
5
10
2

Explanation:

Step1: Recall decay formula

The formula for radioactive - decay is $N = N_0(\frac{1}{2})^n$, where $N$ is the final amount, $N_0$ is the initial amount, and $n$ is the number of half - lives. Given that $N=\frac{1}{32}N_0$, we substitute into the formula: $\frac{1}{32}N_0=N_0(\frac{1}{2})^n$.

Step2: Solve for $n$

Divide both sides of the equation $\frac{1}{32}N_0=N_0(\frac{1}{2})^n$ by $N_0$ (since $N_0
eq0$), we get $\frac{1}{32}=(\frac{1}{2})^n$. Since $\frac{1}{32}=\frac{1}{2^5}=(\frac{1}{2})^5$, then $n = 5$.

Step3: Assume a half - life value (not given in the problem, but if we assume a half - life of 2 units of time for illustration purposes)

If the half - life $t_{1/2}=2$ (assuming the unit of time is appropriate), and the total time $t=nt_{1/2}$. Substituting $n = 5$ and $t_{1/2}=2$ into the formula, we get $t=5\times2 = 10$.

Answer:

10